1 the 'map designer' and do not use the 'random colonisable' planet type (you did specify random map ie not knowing what the map layout is)

2 create a mod with a altered galaxyscenariodef.galaxyscenariodef that removes the dwarfs and asteriods from the random colonisable, (this would allow you to play all existing maps that use the random colonisable (in theory)

Is there any way to make all of the planets normal sized planets (ex: no asteroids, or dwarf planets), save for the pirate base?

Yes. Make a map in the map designer where you use planet types that do spawn moons or asteroid (RandomTrue or the explict Terran/Desert etc. would work).

However, by default each homeworld has a "Starting Area" that includes asteroids and moons. To get rid of these, you'll need to save the map, then open it in Notepad and manually remove the asteroid and moon references from the starting area.